structural behaviors of reinforced concrete piers rehabilitated with...

Research ArticleStructural Behaviors of Reinforced Concrete Piers Rehabilitatedwith FRP Wraps

Junsuk Kang

Department of Landscape Architecture and Rural Systems Engineering Seoul National University Seoul 08826 Republic of Korea

Correspondence should be addressed to Junsuk Kang junkangsnuackr

Received 20 August 2017 Revised 13 October 2017 Accepted 24 October 2017 Published 19 November 2017

Academic Editor Nobuhiro Kawatsuki

Copyright copy 2017 Junsuk KangThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The use of fiber-reinforced polymer (FRP) wraps to retrofit and strengthen existing structures such as reinforced concrete piers isbecoming popular due to the higher tensile strength durability and flexibility gained and the methodrsquos ease of handling and lowinstallation and maintenance costs As yet however few guidelines have been developed for determining the optimum thicknessesof the FRP wraps applied to external surfaces of concrete or masonry structures In this study nonlinear pushover finite elementanalyses were utilized to analyze the complex structural behaviors of FRP-wrapped reinforced rectangular piers Design parameterssuch as pier section sizes pier heights pier cap lengths compressive strengths of concrete and the thicknesses of the FRP wrapsused were thoroughly tested under incremental lateral and vertical loads The results provide useful guidelines for analyzing anddesigning appropriate FRP wraps for existing concrete piers

1 Introduction

The use of fiber-reinforced polymer (FRP) wraps to retrofitand strengthen existing deteriorating concrete or masonrystructures is attractive as these lightweight materials improvetensile strength durability and flexibility are easy to handleand incur low installation and maintenance costs [1] FRPmaterials are thus increasingly being used to enhance orrestore the load-carrying capacity ductility and seismicresistance of a wide range of structures A FRP sheet orlaminate is composed of uniaxial fibers stacked in variousfiber arrangements such as 0∘90∘ or 0∘90∘+45∘minus45∘ toovercome the anisotropic behavior of uniaxial FRP wrapsand embedded in an epoxy resin matrix [1] A number ofdifferent fibers including carbon aramid glass basalt ornatural fibers can be usedThe properties of the resulting FRPwrap can therefore be optimized using various arrangementsand materials according to the strength stiffness or ductilityrequired by a specific application The type of structure forexample whether it consists of beams columns andor slabsmust also be considered

A great deal of research [2ndash6] has been done to investigatethe benefits to be gained by applying FRP materials to pier

structures but as yet no detailed design guidelines have beendeveloped for the optimum thicknesses of the FRP wrapsto be used There have also been no evaluations reported ofthe structural effects of FRP wraps for reinforced concretepiers or columns Although the American Concrete Institute(ACI) [7] has provided some guidelines for noncircularconcrete columns it is not easy to predict the interactionsbetween the piers and pier caps in pier systems using currentACI guidelines This study therefore focused on the retrofitand rehabilitation of existing reinforced concrete piers usingcarbon-based FRP wraps Figure 1 shows how FRP wrapsare normally applied to existing reinforced concrete columns[1 8] which is generally done to enhance the shear strengthof the structure This study investigated the effects of FRPwraps on a number of different important structural charac-teristics such as stiffness strength and ductilityThe primaryobjective of this study was to evaluate the optimum thicknessfor the FRP wraps and the resulting structural effects forexisting rectangular concrete piers Accurate information onthe thickness of the FRP wraps needed for various types andconditions of structures is essential for designers and practi-tioners when selecting FRP systems whose performance willsatisfy their requirements

HindawiInternational Journal of Polymer ScienceVolume 2017 Article ID 2989238 14 pageshttpsdoiorg10115520172989238

2 International Journal of Polymer Science

(a) Shear strengthening by FRP wraps [1] (b) Structural technologies httpswwwvslnetservicestrengthening [8]

Stre

ss

Fiber

FRP composite

Matrix

Strain

Steel

(c) Typical stress-strain curves for fiber matrix steel and FRPcomposite

Figure 1 Application methods and properties of FRP wraps

2 Background

Infrastructure elements across the globe have been deemedstructurally deficient in recent years due to deteriorationwith some becoming functionally obsolete due to theincreased loads they are expected to carry In the case ofdegraded bridge structures this can be a costly exercise as it isoften necessary for the entire substructure not just the super-structure to be demolished and replaced Given the expenseand length of time involved for new construction attemptsare now being made to retrofit and rehabilitate existing sub-structures which can be a viable option in the following cases(1) highway bridges are repurposed to become pedestrian oranimal bridges (2) bridge construction needs to be accel-erated and (3) the demolition of the existing substructurewill have a critically adverse impact on the local ecologicalenvironment

The use of FRP materials for retrofitting and strengthen-ing deteriorated concrete structures has become an increas-ingly attractive proposition due to their superior characteris-tics FRP composites are consisted of layers of fibers embed-ded in a resin matrix the fibers provide strength and stiffness

and the matrix (generally an epoxy resin) protects the fibersfrom abrasion or damage and transfers stresses between thefibers Figure 1(c) shows a set of typical stress-strain curvesfor the fibers and matrix individually and for the resultingFRP composite As the figure demonstrates the stress-straincurves for the FRP composite falls between those for the fiberand matrix curves The properties of FRP composites areaffected by the fiber quality orientation and shape volumeratio and manufacturing conditions and FRP products canbe produced in the form of plates sheets or rods If donecorrectly the application of FRP wraps to existing reinforcedconcrete columns will increase their strength as well as theirductility by confining the concrete thus inducing triaxialstress within the concrete structure The overall effects ofadding FRP wraps to columns or piers should however beevaluated by considering the structural system as a wholeincluding both the piers and the pier cap rather than testingjust an isolated column The complex interactions betweenthe piers and the pier cap associated with various loadingand geometry conditions need to be thoroughly investigatedto confirm the effectiveness or otherwise of installing FRPwraps

International Journal of Polymer Science 3

Table 1 Material properties for FRP wraps [7]

Thickness per ply 0033 cm (0013 in)Ultimate tensile strength 3792MPa (550 ksi)Rupture strain 00167 cmcmModulus of elasticity 227GPa (33000 ksi)Poissonrsquos ratio 03Coefficient of thermal expansion 6500119864 minus 6Shear modulus 87GPa (12692 ksi)

3 Analytical Study

31 FRP Materials The carbon-based FRP materials used inthe example given in ACI 4402R-08 [7] were also utilizedin this study their properties are listed in Table 1 Thestacking sequence of each FRP ply is assumed to be balancedfor example either 0∘90∘ or 0∘90∘+45∘minus45∘ hence theanisotropic behavior of each FRP ply is assumed to cancel outacross each sample and the FRP wraps are considered to beflexible sheets As the stress-strain curves in Figure 1(c) showFRP composites have a higher ultimate strength and lowerstrain at failure than steel

32 Finite Element (FE) Models The SAP2000 finite elementanalysis software [9] was used to perform a nonlinear incre-mental analysis of the structural elements as this software isone of the most used software systems by bridge engineersfor nonlinear static analysis of highway bridges [10] Shataratet al [11] evaluated the effects of plastic hinge for four oldhighway bridges through hinge models and pushover anal-yses in the SAP 2000 Their studies however were limited toflexure dominated conventionally reinforced concrete bridgepiers Kulkarni and Karadi [12] analyzed the existing bridgesusing nonlinear pushover analysis through the SAP 2000Their studies considered both vertical and lateral pushoveranalyses Kappos et al [13] performed various pushoveranalyses such as pushover analysis modal pushover analysisand nonlinear time history analysis using the SAP 200 andconcluded that all three methods yield similar maximumpier top inelastic displacements In the SAP 2000 softwarethe nonlinear structural behavior of structural componentsfor pushover analysis can be simulated through nonlinearpredetermined plastic hinge properties according to Caltranshinge model [14] and FEMA [15 16] Therefore this studyadopted these plastic hinge models through the SAP 2000 Inaddition nonlinear material properties were considered forboth concrete and FRP material in this study as the failuremechanism of these pier systems is highly affected by thenonlinearity of each structural material [17]

The schematic FE models are shown in Figure 2 The 2-dimensional frame system shown in Figure 2(a) representsa typical arrangement of two piers and their associated piercap The boundary conditions for the bottoms of piers areassumed to be fixed and incremental vertical and horizontalloads are applied on the pier-pier cap system separatelyBeam elements are used for the piers and pier caps both ofwhich have square sections as shown in Figure 2(b) A typical

Table 2 Data matrix for pier systems

Type 119882(m)

119867(m)

Pier section(m timesm)

Slender pier system(119882 lt 119867) 6 9

09 times 0912 times 1215 times 1518 times 18





Wide pier system(119882 gt 119867) 9 6




deformed shape for a pier system subjected to a lateral loadis shown in Figure 2(c) Note that the FRP wraps shown inFigure 2(b) are applied only to the piers not the pier capThe adequate input of nonlinearmaterial properties in the FEanalyses is critical to evaluate complex nonlinear structuralbehaviors of the whole pier systems Figure 3 shows thenonlinearmaterial properties for the FRPwraps and concreteused in the analysis The FRP behaviors are assumed to bethe same for both tensile and compressive loads and thecompressive and tensile behaviors of concrete are assumedto be as shown in Figure 3(b) The various configurations forpier systems and sections tested are shown in Table 2 Herea pier system with a pier height 119867 that is longer than thelength of the pier cap 119882 is categorized as a slender piersystem while a pier system whose pier cap (119882) is longerthan the height of pier (119867) is considered to be a wide piersystem The typical dimensions given for piers pier cap andpier sections are adopted from information on bridges in theUS state ofGeorgia and cover the upper and lower boundariesfor most pier systems

33 Pushover Analysis This study adopted nonlinear staticpushover analysis to evaluate all the stages of failure mech-anism for reinforced concrete piers rehabilitated with FRPwraps Static pushover analysis is usually used to estimatethe structural performance of structures subjected to earth-quakes via a static inelastic analysis [9] with the appliedincremental lateral loads representing earthquake inducedforces In this study the incremental loadings were applied


Pier cap

Pier Pier

W

H

Fixed Fixed

PV

PH

(a) Geometry loading and boundary condi-tions of structure

10 rebar

FRP

Concrete

(b) Example of square pier section details

Plastic hinge

Z

X

(c) Typical deformed shape under lateral loads

Figure 2 FE model development (119875119867 = incremental lateral load 119875119881 = incremental vertical load119882 = length of pier cap and119867 = height ofpier)

(a) Carbon-based FRP wrap (unit of stress ksi) (b) Concrete (1198911015840119888 = 6000 psi (414MPa))

Figure 3 Stress-strain curve inputs used in the analyses

at the top of the left hand piers as shown in Figure 2(a) Aplot of the total base shear or reaction versus associated lateralor vertical displacements at the monitoring node is producedwhere the capacities of the pier systems are represented byload-displacement curves This analysis therefore examinesthe ultimate strength stiffness and ductility capacity for thatspecific pier system configuration

4 Analytical Results and Discussion

41 Vertical Load Applications The structural stability of piersystems was investigated by applying incremental vertical

loads to the top of the left hand pier as the unsymmetricloading conditions would provide conservative results Allpier sections are square with dimensions ranging from09m by 09m to 18m by 18m as given in Table 2 Theheight of the piers (H) and the length of the pier cap (119882)are taken to be 6m (195 ft) and 12m (39 ft) respectivelyThe compressive strengths of the concrete investigated are21MPa (3000 psi) 28MPa (4000 psi) 34MPa (5000 psi)and 41MPa (6000 psi) which cover the most typical com-pressive strengths of concrete used in the highway bridgepiers The thickness of the carbon FRP wraps is takento be 33 cm (13 in 100 plies) which is considered to


0

20

40

60

0 05 1 15 2

W FRPNo FRP

ΔV (cm)

PV

(MN

)

(a) 1198911015840119888 = 21MPa (3000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(c) 1198911015840119888 = 34MPa (5000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(d) 1198911015840119888 = 41MPa (6000 psi)

Figure 4 Pier section (09m by 09m) subjected to vertical loads (thickness of FRP wrap = 33 cm)

be relatively thick Therefore the ultimate effects of FRPwraps for the strength stiffness and deformation capacitiescould be evaluated through this study The vertical load-displacement history can then be plotted to evaluate thepier systemsrsquo strength stiffness and deformation capacitiesFigure 4 shows the structural performance of a pier systemcomposed of 09m by 09m piers subjected to incrementalvertical loads The piers wrapped with FRP laminates arecompared to those without FRP sheets As shown in Figure 4the ultimate strengths of the pier systems remain the samewhen the piers are rehabilitated with FRP wraps and thistrend is consistent across all the compressive loads testedwhich indicates that the thick FRP wraps did not increase thecompressive ultimate strengths of the pier system Howeverthe stiffness which is defined as the slope in the linear regionof the force-displacement response approximately doubleswith the FRP applications in all cases As long as the loaddemand remains the same for the intended use of the piersystem it may not be necessary to increase its ultimate

strength The increased stiffness will enhance the structuralstability of the system which may well coincide with thedesired benefit to be gained via the FRP wrap application

For systems with larger pier cross-sections the datapresented in Figures 5ndash7 confirm that the ultimate strengthsof the pier systems do not change with the installation ofthe FRP wraps Interestingly the stiffness of the systemapproximately doubles in every case except the largest piersection 18m by 18m which showed only a 50 increasecompared to the pier without FRP wraps

42 Lateral Load Applications for Slender Pier SystemsFollowing the same procedure as that described above forvertical load cases models were designed and subjected toa lateral load Due to the fact that lateral loads are highlyimportant for a bridgersquos performance a closer look at theeffect of different FRP properties was carried out focusingspecifically on the thickness layering and material used


0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)


The incremental lateral loads were applied at the top ofthe left hand piers to evaluate the expected performance ofthe slender pier systems As for the vertical loading caselateral load-displacement curves were plotted to identify theultimate strengths stiffness and deformation capacity of theslender pier systems

Figure 8 shows the effect of varying the FRP wrapthickness on the structural performance of a slender piersystem with 119882 = 6m and 119867 = 9m Two pier sections09m by 09m and 12m by 12m were investigated forFRP thicknesses ranging from zero to 66 cm As shown inFigures 8(a) and 8(b) both the stiffness and the ultimatestrengths of the slender pier systems increased with theaddition of FRP wraps In particular the FRP wraps withthicknesses greater than 33 cm clearly enhanced the stiffnessandultimate strengths of the systemas awhole Similar trendswere shown in the other two slender systems tested namely119882 = 6m and119867 = 12m (Figure 9) and119882 = 9m and119867 = 12m

(Figure 10) The compressive strength used for the curvesshown in Figures 8ndash10 was 41 MPa (6000 psi)

43 Lateral Load Applications for Wide Pier Systems Widepier systems with119882 larger than119867 were also investigated forvarious thicknesses of FRP wraps As shown in Figure 11 thestiffness of the system was again enhanced by the additionof the FRP wraps The ultimate strengths of the wide piersystem having119882 = 9m and119867 = 6m increased considerablyalthough some cases did not achieve convergence due to theerrors The ultimate strengths of the wide pier system witha pier section of 12m by 12m (Figure 12) were dispropor-tionally increased relative to the thicknesses of the FRPwrapsapplied The largest wide pier section tested (15m by 15m)exhibited only an insignificant effect on the ultimate strengthexcept for the thickest FRP tested 66 cm Overall a wide piersystem with an intermediate section size of the order of 12mby 12m is likely to benefit most from rehabilitation with FRP


0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)


wraps especially compared to the slender pier systems wherethe benefits gained were less obvious

44 Summary of Structural Effects of FRP Wraps The struc-tural effects of the FRP wraps for the pier systems subjectedto incremental lateral loads are summarized in Figure 13 fora pier with a section of 09m by 09m which builds on theinsights provided by the data presented in Figures 8ndash12 forall the pier section sizes The yield points are unclear withsome cases exhibiting multiple yield points so as definedin Figure 13(a) the stiffness 1st yield point 2nd yield pointand ultimate strength are evaluated separately to provide in-depth analyses of the structural effects of applying FRP wrapsto the pier systems As shown in Figure 13(b) the wide piersystems are affected more strongly by the addition of FRPwraps than the slender pier systems However the 1st and 2ndyield strengths of the pier systems do not change significantly

even as the thickness of the FRP wraps increases Examiningthe ultimate strengths shown in Figure 13(e) the wider piersystem is the only one strongly affected by the FRP thickness

5 Simplified 119875-119872 Interaction Diagrams

51 ACI Procedures The ACI provides general guidelines forthe analysis and design of reinforced concrete column withFRP wraps surrounding each memberrsquos cross-sectional area[7] According to their recommended procedure the axialand bending behaviors before and after rehabilitation shouldbe analyzed by calculating the interaction diagrams priorto the addition of FRP and afterwards then comparing theresults119875-119872 interaction diagrams are constructed based on the

principles of equilibrium and strain compatibility of conven-tional reinforced concrete columns considering the stress-strain relationship for FRP-wrapped reinforced concrete [18]


0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)


They can be reduced to two bilinear curves passing throughthe following three points [7]

(i) Point A (pure compression) at a uniform axial com-pressive strain of confined concrete

(ii) Point B with a strain distribution corresponding tozero strain

(iii) Point C with a strain distribution corresponding tobalanced failure with a maximum compressive strainand a yielding tensile strain

For FRP-wrapped concrete with existing steel-tie reinforce-ment the values of 120601119875119899(A) corresponding to Point A are asfollows

120601119875119899(A) = 08120601 (0851198911015840119888119888 (119860119892 minus 119860 119904119905) + 119891119910119860 119904119905) (1)

The coordinates of Points B and C can be calculated as

120601119875119899(BC) = 120601 [(119860 (119910119905)3 + 119861 (119910119905)

2 + 119862 (119910119905) + 119863)

+sum119860 119904119894119891119904119894]

120601119872119899(BC)

= 120601 [(119864 (119910119905)4 + 119865 (119910119905)

3 + 119866 (119910119905)2 + 119867 (119910119905) + 119868)

+sum119860 119904119894119891119904119894119889119894]

(2)

The coefficientsA BCD E FGH and I in these equationscan be calculated from ACI 4402Rrsquos [7 Eq (D-3)] Designexamples reflecting the recommended ACI procedures arepresented in the following section

Theprimary objective of presenting theseACI proceduresand design examples here is to highlight the differences


0

500

1000

1500

0 5 10 15 20 25

No FRP

PH

(kN

)

17 ＝Ｇ FRP41 ＝Ｇ FRP

66 ＝Ｇ FRP07 ＝Ｇ FRP33 ＝Ｇ FRP

5 ＝Ｇ FRP

ΔH (cm)

(a) Pier section 09m by 09m

0

1000

2000

3000

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)

(b) Pier section 12m by 12m

Figure 8 Slender pier system with119882 = 6m and119867 = 9m (1198911015840119888 = 41MPa)

0

500

1000

0 10 20 30

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

4000

5000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



between theoretical approaches that simply consider isolatedcolumnmembers andfinite element approaches that considerentire systems and include both piers and pier caps

52 Design Examples Noncircular reinforced concretecolumns with square cross-sections with dimensions ofeither 03m by 03m or 06m by 06m containing 10 rebarwere selected to examine the contribution of FRP wrapapplications in axial and bending performances in differentsituation The ACI procedures were programmed usingExcel to develop simplified 119875-119872 interaction diagrams forvarious compressive strengths of concrete numbers of rebarand numbers of FRP plies Figure 14 shows simplified 119875-119872

interaction diagrams for rectangular reinforced concretecolumns both with and without FRP of various types Notethat the tensile strength of concrete is neglected in thesediagrams The design parameters considered in the analysesare the size of the pier section and the variables listed abovenamely the compressive strength of the concrete amount ofrebar used and the number of FRP plies

Figure 14 shows the strength enhancements due to theinclusion of the FRP wraps in the compression-controlledzone The piers with the larger section of 06m by 06m(Figures 14(a) and 14(b)) showed significantly enhancedstrengths compared to the smaller 03m by 03m piers(Figures 14(c) and 14(d))


0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)


Figure 11 Wide pier system with119882 = 9m and119867 = 6m (1198911015840119888 = 41MPa)

6 Conclusions

The analytical study presented here compared pier sys-tems composed of FRP-wrapped square reinforced concretecolumns topped by pier caps to evaluate the structuraleffects induced by the application of the FRP materials Anonlinear pushover analysis was implemented in conjunctionwith FE methods ACI procedures and examples were alsopresented for comparison Various configurations of the piersystems were considered to cover most practical cases Verti-cal and horizontal load-displacement curves were produced

to estimate the ultimate strength stiffness yield strengthand deformation capacity of the resulting pier systems Thefollowing conclusions can be drawn from the results of thisanalysis

(1) The FE models developed for this study successfullyevaluated the complex interactions between piersand pier caps associated with the addition of theFRP wraps overcoming the limitations of existingtheoretical approaches The elastic yield ultimate


0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)

No FRP17 ＝Ｇ FRP41 ＝Ｇ FRP


5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)

(c) Pier section 15m by 15m


and postfailing stages were readily evaluated by con-sidering nonlinear material properties and geometricnonlinearity

(2) The stiffness of a pier systemunder vertical incremen-tal loads doubled with the addition of FRPwraps witha thickness of 33 cmThe ultimate strength howeverdid not change significantly Overall the applicationof the FRP wraps enhances the vertical stability ofa pier system due to the major improvement in thestiffness

(3) The ultimate strength and stiffness of a pier systemunder incremental lateral loads increased due to theFRP wraps Wider pier systems with an intermediatecross-sectional size of the order of 12m by 12m areparticularly well suited to rehabilitation with FRPwraps benefitting substantially more than slenderpier systems

(4) The design examples presented here calculatedaccording to the ACIrsquos recommended proceduresconfirmed that the strength enhancement inducedby FRP application lies entirely in the compression-controlled region which is a limitation of thetheoretical approach This limitation means that theeffects of the tensile strength of concrete which areusually neglected in the simplified 119875-119872 interactiondiagrams normally used can easily be taken intoaccount using the FE analysis presented in this paper

Conflicts of Interest

The author declares that he has no conflicts of interest

Acknowledgments

This work was supported by 2016 Georgia Southern Univer-sity Senior Project 2017 Seoul National University Invitation


Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ

W = 12ＧH = 9Ｇ (slender)

H = 6Ｇ (wide)W = 6Ｇ

W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)

(b) Stiffness (119896)

0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)

(c) 1st yield strength (1198651119910)

0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

(d) 2nd yield strength (1198652119910)

0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

(e) Ultimate strength (119865119906)

Figure 13 Effects of FRP thicknesses for various geometries of pier systems (pier section = 09m by 09m 119905frp = thickness of FRP wrap)


0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)

(a) Pier dimension 06mby 06m119873119903 = 12119873frp = 6 and1198911015840119888 = 6500 psi

Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)

(b) Pier dimension 06m by 06m 119873119903 = 12 119873frp = 4 and 1198911015840119888 =4000 psi

Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)

(c) Pier dimension 03m by 03m 119873119903 = 12 119873frp = 3 and 1198911015840119888 =6500 psi

Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)

(d) Pier dimension 03m by 03m 119873119903 = 12 119873frp = 3 and 1198911015840119888 =4000 psi

Figure 14 Simplified 119875-119872 interaction diagrams for rectangular reinforced concrete columns (119873119903 = amount of rebar119873frp = number of FRPplies and 1198911015840119888 = compressive strength of concrete)

Program for Distinguished Scholar and a grant funded byMinistry of Land Infrastructure and Transport (MOLIT) ofKorea Agency for Infrastructure Technology Advancement(KAIA) (17CTAP-C132633-01)

References

[1] A Balsamo G P Ludovico A Prota G Manfredi and ECosenza Composites for Structural Strengthening Wiley Ency-clopedia of Composites 2nd edition 2012

[2] M N S Hadi ldquoBehaviour of FRP strengthened concrete col-umns under eccentric compression loadingrdquo Composite Struc-tures vol 77 no 1 pp 92ndash96 2007

[3] A B Pridmore and V M Karbhari Structural Response of nearSurfaceMounted CFRP Strengthened Reinforced Concrete BridgeDeck Overhang California Department of Transportation SanDiego Calif USA 2008

[4] S E Gunaslan and H Karasin ldquoUse of FRP composite mate-rial for strengthening reinforced concreterdquo European ScientificJournal vol 10 2014

[5] A K Chauhan and N B Umravia ldquoStrengthening of Rein-forced Concrete Columns Using FRPrdquo International Journal ofGlobal Technology Initiatives vol 1 no 1 2012

[6] T Alkhrdaji ldquoStrengthening of concrete structures using FRPcompositesrdquo Structure Magazine pp 18ndash20 2015


[7] ACI 4402R-08Guide for the Design And Construction of Exter-nally Bonded FRP Systems for Strengthening Concrete StructuresAmerican Concrete Institute Detroit Mi USA 2008

[8] StructuralTechnologies 2016httpswwwvslnetservicestrength-ening

[9] CSI Reference Manual on SAP2000 Computers and StructuresInc Walnut Creek Calif USA 2017

[10] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008

[11] N Shatarat M Shehadeh and M Naser ldquoImpact of plastichinge properties on capacity curve of reinforced concretebridgesrdquo Advances in Materials Science and Engineering vol2017 Article ID 6310321 13 pages 2017

[12] S Kulkarni and U N Karadi ldquoNonlinear analysis of existing rcbridge using SAP 2000rdquo Civil and Environmental Research vol6 no 12 2014

[13] A J Kappos T S Pardaskeva and A G Sextos ldquoModal push-over analysis as a means for the seismic assessment of bridgestructuresrdquo in Proceedings of the 4th European Workshop on theSeismic Behaviour of Irregular andComplex Structures Paper no49 2005

[14] Caltrans ldquoCaltrans seismic design criteriardquo Tech Rep 1California Department of Transportation 2010

[15] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000

[16] FHWA ldquoSeismic retrofitting manual for highway structurespart 1- bridgesrdquo Publication vol No pp 06ndash032 2006

[17] K Sethy ldquoApplication of Pushover Analysis to RC BridgesrdquoTech Rep Department of Civil Engineering National Instituteof Technology Rourkela India 2011

[18] S Rocca N Galati and A Nanni ldquoInteraction diagrammethodology for design of FRP-confined reinforced concretecolumnsrdquo Construction and Building Materials vol 23 no 4pp 1508ndash1520 2009

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of



(a) Shear strengthening by FRP wraps [1] (b) Structural technologies httpswwwvslnetservicestrengthening [8]

Stre

ss

Fiber

FRP composite

Matrix

Strain

Steel

(c) Typical stress-strain curves for fiber matrix steel and FRPcomposite

Figure 1 Application methods and properties of FRP wraps

2 Background

Infrastructure elements across the globe have been deemedstructurally deficient in recent years due to deteriorationwith some becoming functionally obsolete due to theincreased loads they are expected to carry In the case ofdegraded bridge structures this can be a costly exercise as it isoften necessary for the entire substructure not just the super-structure to be demolished and replaced Given the expenseand length of time involved for new construction attemptsare now being made to retrofit and rehabilitate existing sub-structures which can be a viable option in the following cases(1) highway bridges are repurposed to become pedestrian oranimal bridges (2) bridge construction needs to be accel-erated and (3) the demolition of the existing substructurewill have a critically adverse impact on the local ecologicalenvironment

The use of FRP materials for retrofitting and strengthen-ing deteriorated concrete structures has become an increas-ingly attractive proposition due to their superior characteris-tics FRP composites are consisted of layers of fibers embed-ded in a resin matrix the fibers provide strength and stiffness

and the matrix (generally an epoxy resin) protects the fibersfrom abrasion or damage and transfers stresses between thefibers Figure 1(c) shows a set of typical stress-strain curvesfor the fibers and matrix individually and for the resultingFRP composite As the figure demonstrates the stress-straincurves for the FRP composite falls between those for the fiberand matrix curves The properties of FRP composites areaffected by the fiber quality orientation and shape volumeratio and manufacturing conditions and FRP products canbe produced in the form of plates sheets or rods If donecorrectly the application of FRP wraps to existing reinforcedconcrete columns will increase their strength as well as theirductility by confining the concrete thus inducing triaxialstress within the concrete structure The overall effects ofadding FRP wraps to columns or piers should however beevaluated by considering the structural system as a wholeincluding both the piers and the pier cap rather than testingjust an isolated column The complex interactions betweenthe piers and the pier cap associated with various loadingand geometry conditions need to be thoroughly investigatedto confirm the effectiveness or otherwise of installing FRPwraps




3 Analytical Study





Type 119882(m)

119867(m)















Pier cap

Pier Pier

W

H

Fixed Fixed

PV

PH


10 rebar

FRP

Concrete


Plastic hinge

Z

X










0

20

40

60

0 05 1 15 2

W FRPNo FRP

ΔV (cm)

PV

(MN

)

(a) 1198911015840119888 = 21MPa (3000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(c) 1198911015840119888 = 34MPa (5000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(d) 1198911015840119888 = 41MPa (6000 psi)







0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)









0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







120601119875119899(A) = 08120601 (0851198911015840119888119888 (119860119892 minus 119860 119904119905) + 119891119910119860 119904119905) (1)


120601119875119899(BC) = 120601 [(119860 (119910119905)3 + 119861 (119910119905)

2 + 119862 (119910119905) + 119863)

+sum119860 119904119894119891119904119894]

120601119872119899(BC)

= 120601 [(119864 (119910119905)4 + 119865 (119910119905)

3 + 119866 (119910119905)2 + 119867 (119910119905) + 119868)

+sum119860 119904119894119891119904119894119889119894]

(2)




0

500

1000

1500

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

0 10 20 30

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

4000

5000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)








0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)



6 Conclusions





0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of





3 Analytical Study





Type 119882(m)

119867(m)















Pier cap

Pier Pier

W

H

Fixed Fixed

PV

PH


10 rebar

FRP

Concrete


Plastic hinge

Z

X










0

20

40

60

0 05 1 15 2

W FRPNo FRP

ΔV (cm)

PV

(MN

)

(a) 1198911015840119888 = 21MPa (3000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(c) 1198911015840119888 = 34MPa (5000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(d) 1198911015840119888 = 41MPa (6000 psi)







0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)









0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







120601119875119899(A) = 08120601 (0851198911015840119888119888 (119860119892 minus 119860 119904119905) + 119891119910119860 119904119905) (1)


120601119875119899(BC) = 120601 [(119860 (119910119905)3 + 119861 (119910119905)

2 + 119862 (119910119905) + 119863)

+sum119860 119904119894119891119904119894]

120601119872119899(BC)

= 120601 [(119864 (119910119905)4 + 119865 (119910119905)

3 + 119866 (119910119905)2 + 119867 (119910119905) + 119868)

+sum119860 119904119894119891119904119894119889119894]

(2)




0

500

1000

1500

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

0 10 20 30

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

4000

5000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)








0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)



6 Conclusions





0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



Pier cap

Pier Pier

W

H

Fixed Fixed

PV

PH


10 rebar

FRP

Concrete


Plastic hinge

Z

X










0

20

40

60

0 05 1 15 2

W FRPNo FRP

ΔV (cm)

PV

(MN

)

(a) 1198911015840119888 = 21MPa (3000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(c) 1198911015840119888 = 34MPa (5000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(d) 1198911015840119888 = 41MPa (6000 psi)







0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)









0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







120601119875119899(A) = 08120601 (0851198911015840119888119888 (119860119892 minus 119860 119904119905) + 119891119910119860 119904119905) (1)


120601119875119899(BC) = 120601 [(119860 (119910119905)3 + 119861 (119910119905)

2 + 119862 (119910119905) + 119863)

+sum119860 119904119894119891119904119894]

120601119872119899(BC)

= 120601 [(119864 (119910119905)4 + 119865 (119910119905)

3 + 119866 (119910119905)2 + 119867 (119910119905) + 119868)

+sum119860 119904119894119891119904119894119889119894]

(2)




0

500

1000

1500

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

0 10 20 30

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

4000

5000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)








0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)



6 Conclusions





0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



0

20

40

60

0 05 1 15 2

W FRPNo FRP

ΔV (cm)

PV

(MN

)

(a) 1198911015840119888 = 21MPa (3000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(c) 1198911015840119888 = 34MPa (5000 psi)

W FRPNo FRP

0

20

40

60

0 05 1 15 2ΔV (cm)

PV

(MN

)

(d) 1198911015840119888 = 41MPa (6000 psi)







0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)









0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







120601119875119899(A) = 08120601 (0851198911015840119888119888 (119860119892 minus 119860 119904119905) + 119891119910119860 119904119905) (1)


120601119875119899(BC) = 120601 [(119860 (119910119905)3 + 119861 (119910119905)

2 + 119862 (119910119905) + 119863)

+sum119860 119904119894119891119904119894]

120601119872119899(BC)

= 120601 [(119864 (119910119905)4 + 119865 (119910119905)

3 + 119866 (119910119905)2 + 119867 (119910119905) + 119868)

+sum119860 119904119894119891119904119894119889119894]

(2)




0

500

1000

1500

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

0 10 20 30

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

4000

5000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)








0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)



6 Conclusions





0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

20

40

60

80

100

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)









0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







120601119875119899(A) = 08120601 (0851198911015840119888119888 (119860119892 minus 119860 119904119905) + 119891119910119860 119904119905) (1)


120601119875119899(BC) = 120601 [(119860 (119910119905)3 + 119861 (119910119905)

2 + 119862 (119910119905) + 119863)

+sum119860 119904119894119891119904119894]

120601119872119899(BC)

= 120601 [(119864 (119910119905)4 + 119865 (119910119905)

3 + 119866 (119910119905)2 + 119867 (119910119905) + 119868)

+sum119860 119904119894119891119904119894119889119894]

(2)




0

500

1000

1500

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

0 10 20 30

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

4000

5000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)








0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)



6 Conclusions





0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

30

60

90

120

150

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)









0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







120601119875119899(A) = 08120601 (0851198911015840119888119888 (119860119892 minus 119860 119904119905) + 119891119910119860 119904119905) (1)


120601119875119899(BC) = 120601 [(119860 (119910119905)3 + 119861 (119910119905)

2 + 119862 (119910119905) + 119863)

+sum119860 119904119894119891119904119894]

120601119872119899(BC)

= 120601 [(119864 (119910119905)4 + 119865 (119910119905)

3 + 119866 (119910119905)2 + 119867 (119910119905) + 119868)

+sum119860 119904119894119891119904119894119889119894]

(2)




0

500

1000

1500

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

0 10 20 30

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

4000

5000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)








0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)



6 Conclusions





0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(a) 1198911015840119888 = 21MPa (3000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(b) 1198911015840119888 = 28MPa (4000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(c) 1198911015840119888 = 34MPa (5000 psi)

0

50

100

150

200

0 05 1 15 2

W FRPNo FRP

PV

(MN

)

ΔV (cm)

(d) 1198911015840119888 = 41MPa (6000 psi)







120601119875119899(A) = 08120601 (0851198911015840119888119888 (119860119892 minus 119860 119904119905) + 119891119910119860 119904119905) (1)


120601119875119899(BC) = 120601 [(119860 (119910119905)3 + 119861 (119910119905)

2 + 119862 (119910119905) + 119863)

+sum119860 119904119894119891119904119894]

120601119872119899(BC)

= 120601 [(119864 (119910119905)4 + 119865 (119910119905)

3 + 119866 (119910119905)2 + 119867 (119910119905) + 119868)

+sum119860 119904119894119891119904119894119889119894]

(2)




0

500

1000

1500

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

0 10 20 30

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

4000

5000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)








0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)



6 Conclusions





0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



0

500

1000

1500

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

0 5 10 15 20 25

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

0 10 20 30

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

1000

2000

3000

4000

5000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)








0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)



6 Conclusions





0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



0

500

1000

0 10 20 30 40 50

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

500

1000

1500

2000

0 10 20 30 40

No FRP

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)



0

500

1000

1500

2000

0 2 4 6 8 10

PH

(kN

)

No FRP


ΔH (cm)


0

1000

2000

3000

4000

0 2 4 6 8 10

No FRP

PH

(kN

)


5 ＝Ｇ FRP

ΔH (cm)



6 Conclusions





0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



0

1000

2000

3000

4000

0 5 10 15

PH

(kN

)

ΔH (cm)

No FRP



0

4000

8000

12000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)


0

5000

10000

15000

0 5 10 15 20 25

PH

(kN

)



5 ＝Ｇ FRP

ΔH (cm)









Acknowledgments



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



Forc

eDisplacement

F1y

F2y

Fu

k =F1y

Δ1y

Δ1y

(a) Notation

0

2000

4000

6000

0 2 4 6 8

k (k

Nc

m)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

2000

4000

6000

0 5 10

F1y

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)

tＬＪ (cm)


0

1000

2000

3000

4000

0 5 10

2nd

yiel

d str

engt

h (k

N)

tＬＪ (cm)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)


0

1000

2000

3000

4000

0 2 4 6 8tＬＪ (cm)

Fu

(kN

)

W = 9Ｇ

W = 6Ｇ



W = 9Ｇ

H = 12Ｇ (slender)

H = 6Ｇ (wide)

H = 12Ｇ (slender)




0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



0

2

4

6

8

10

12

0 10 20

Without FRPWith FRP

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

2

4

6

8

0 2 4 6 8 10

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

5

0 1 2

Pn

(MN

)

Mn (MN-m)


Without FRPWith FRP

0

1

2

3

4

00 05 10

Pn

(MN

)

Mn (MN-m)




References



























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of






















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


structural behaviors of reinforced concrete piers rehabilitated with...

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